Introduction to (Formal) Logic (and AI)
Spring 2024 Edition of IFLAI1 (“eye” • “fly” • “one”)
Selmer Bringsjord

Table of Contents

Learning logic with patented AI technology.

with Naveen Sundar G.
∧ KB Foushée ∧ \(\ldots\)



Figure 2: Larry


Figure 3: Lucy

[All artwork (all of which is copyrighted) for the LAMA® paradigm by KB Foushée.]

Terminology & General Orientation

This course is an advanced, accelerated introduction to deductive formal logic, with some substantive coverage of inductive formal logic, in which formalisms for dealing with uncertainty (e.g., probability theory, and also the likelihood calculus) are included, and to heterogeneous formal logic (which allows reasoning over not only textual/linguistic content, but visual content as well). The course conforms to the LAMA® paradigm in general, and is specifically based on *Hyperlogic*TM, which among other things (all of which are explained and covered) is based on the view that proofs and arguments are best cast as hypergraphs. Since the present course emphasizes deduction, the course is specifically based on hypergraphical natural deduction. This is the only robust treatment of formal logic based on this form of deduction, which has many unique advantages.

The course makes crucial use of patented AI for learning, and also provides an introduction to AI itself, at least AI of the logicist variety. In particular, and for example, students are exposed to a pure and general form of logic programming (so-called PGLP) that is particularly well-suited for pursuing logicist AI; students are also introduced to the new PGLP programming environment *Hyperlog*®. In addition, students are educated about the part of AI known as automated reasoning, which in general consists in AI itself reasoning in both deductive and inductive fashion.

The last part of the class includes distinctive coverage of some of the great theorems proved by humanity’s greatest logician: Kurt Gödel.


Students will purchase access to (and in the case of the e-textbook, obtain) the inseperably interconnected trio of

  1. HyperGrader®, a comprehensive, patented (Patent No. US 11,526,779 B2) AI platform generating, assessing, tracking, and broadcasting (in anonymized form on leaderboards) problems, the tackling of which largely takes place in
  2. the patented HyperSlate® AI system for (among other things) proof construction in collaboration with AI technology; and
  3. the (copyrighted) e-textbook Logic: A Modern Approach; Beginning Deductive Logic via HyperSlate®, Advanced (LAMA-BDLAHS).

Each member of this trio will be available online after purchase of the relevant code-carrying envelope from or in the RPI Follett Bookstore. Full logistics of this purchase, and the content of the envelope and how to proceed from this content, will be explained in the first class (and subsequently, in greater details, with walk-throughs given live). Updates to LAMA-BDLAHS, and additional exercises, will be provided by listing on relevant LAMA® web pages upon signing in to HyperGrader® (and sometimes by email) through the course of the semester. You will need to manage many electronic files as this course proceeds, and e-housekeeping and e-orderliness are of paramount importance. You will specifically need to assemble a library of completed and partially completed proofs in the cloud so that you can use them as building blocks in harder proofs; in other words, building up your own “logical library” will be crucial. This will be your library in HyperSlate®.

Please note that both HyperGrader® and HyperSlate® are both patented, copyrighted, trademarked AI systems; copying and/or reverse engineering or distributing this software to others is strictly prohibited by law. You will need to AGREE online (after registration) to a License Agreement. This agreement will also cover the e-textbook, which is copyrighted as well, and cannot be copied or distributed in any way, even in part.

In addition, occasionally papers may be assigned as reading. Two, indeed, were assigned in the syllabus, on the first day of class.

As to AI, it’s strongly recommended that students read the online summary of AI provided by Bringsjord & Govindarajulu, available here.

Finally, slide decks used in class will contain crucial additional content above and beyond LAMA-BDLA, information posted on HyperGrader®, and on HyperSlate®; this additional content will be available on the web site as the course unfolds through time.


The version of the course now underway is the Spring 2024 edition, the syllabus for which is available here. This is a robust, detailed syllabus, and is required reading — and reading that will pay off, for sure.


This is the patented intelligent software system used for constructing proofs and arguments in collaboration with AI technology, and is available after registration and sign-in.


This is the patented overarching AI platform (via which HyperSlate® is accessed) for submitting, getting assessed, and earning points for proofs and arguments constructed in HyperSlate®, and is available after registration and by sign-in.


This is the e-textbook for the course, and is obtained after registration and sign-in, by downloading fromm HyperGrader®.

Class-Day Content

Tutorials (expands as semester unfolds)

Pop Problems

These problems are timed and released in HyperGrader® in the absence of any preceding announcement that they are coming. Please see the syllabus for more information.


Homework consists of solving all Required problems listed on HyperGrader®’s web pages. (Non-required problems are clearly marked as such, e.g. as Bonus Problems.) All solutions are created in their final form in HyperSlate®. HyperGrader® for interactive use via its underlying AI technology opens for its Spring 2023 stint on or about Jan 26 2023, and an orientation/introduction to the system is given in class that day. Note that homeworks cannot be done without access to, and sustained and continuous use of, HyperSlate®, access via the AI platform HyperGrader®.


There are three tests, each presented and taken online and outside of class via HyperGrader®. Please see the syllabus for their release dates.



Warning: Increasingly, the term ‘reasoning’ is used by some who don’t really do anything related to reasoning, as traditionally understood, to nonetheless label what they do. Fortunately, it’s easy to verify that some reasoning is that which is covered by formal logic: If the reasoning is explicit; links declarative statements or formulae together via explicit, abstract reasoning schemata or rules of inference (giving rise to at least explicit arguments, and often proofs); is surveyable and inspectable, and ultimately machine-checkable; then the reasoning in question is what formal logic is the science and engineering of. (An immediate consequence of the characteristics just listed is that AIs based on artificial neural networks don’t reason, ever.) In order to characterize /in/formal logic, one can remove from the previous sentence the requirements that the links must conform to explicit reasoning schemas or rules of inference, and machine-checkability. It follows that so-called informal logic would revolve around arguments, but not proofs. An excellent overview of informal logic, which will be completely ignored in this class, is provided in “Informal Logic” in the Stanford Encyclopedia of Philosophy. In this article, it’s made clear that, yes, informal logic concentrates on the nature and uses of argument.

Author: Selmer Bringsjord

Created: 2024-04-22 Mon 16:10

Emacs (Org mode 8.2.10)